A class of identities relating Whittaker and Bessel functions

Identities between Whittaker and modified Bessel functions are derived for particular complex orders. Certain polynomials appear in such identities, which satisfy a fourth order differential equation (not of hypergeometric type), and they themselves can be expressed as particular linear combinations of products of modified Bessel and confluent hypergeometric functions.Comment: 8 pages, late

All higher-dimensional Majumdar-Papapetrou black holes

We prove that the only asymptotically flat spacetimes with a suitably regular event horizon, in a generalised Majumdar-Papapetrou class of solutions to higher-dimensional Einstein-Maxwell theory, are the standard multi-black holes. The proof involves a careful analysis of the near-horizon geometry and an extension of the positive mass theorem to Riemannian manifolds with conical singularities. This completes the classification of asymptotically flat, static, extreme black hole solutions in this theory.Comment: 10 pages. v2: minor correction, assumption added, references added. v3: main result stated as a theorem, published versio

Static near-horizon geometries in five dimensions

We consider the classification of static near-horizon geometries of stationary extremal (not necessarily BPS) black hole solutions of five dimensional Einstein-Maxwell theory coupled to a Chern-Simons term with coupling xi (with xi=1 corresponding to supergravity). Assuming the black holes have two rotational symmetries, we show that their near-horizon geometries are either the direct product AdS_3 X S^2 or a warped product of AdS_2 and compact 3d space. In the AdS_2 case we are able to classify all possible near-horizon geometries with no magnetic fields. There are two such solutions: the direct product AdS_2 X S^3 as well as a warped product of AdS_2 and an inhomogeneous S^3. The latter solution turns out to be near-horizon limit of an extremal Reissner-Nordstrom black hole in an external electric field. In the AdS_2 case with magnetic fields, we reduce the problem (in all cases) to a single non-linear ODE. We show that if there are any purely magnetic solutions of this kind they must have S^1 X S^2 horizon topology, and for xi^2 <1/4 we find examples of solutions with both electric and magnetic fields.Comment: Latex, 28 pages. v2: minor changes, reference adde

Classification of near-horizon geometries of extremal black holes

Any spacetime containing a degenerate Killing horizon, such as an extremal black hole, possesses a well-defined notion of a near-horizon geometry. We review such near-horizon geometry solutions in a variety of dimensions and theories in a unified manner. We discuss various general results including horizon topology and near-horizon symmetry enhancement. We also discuss the status of the classification of near-horizon geometries in theories ranging from vacuum gravity to Einstein-Maxwell theory and supergravity theories. Finally, we discuss applications to the classification of extremal black holes and various related topics. Several new results are presented and open problems are highlighted throughout.Comment: 70 pages; invited review article for Living Reviews in Relativity; v2 some improvements and references adde